A zero coupon bond delivers the investor's entire return through which mechanism?

Periodic interest payments made semi-annually at a fixed rate until maturity

A variable coupon that resets periodically to track prevailing market interest rates

Dividends declared from profits at the discretion of the issuing corporation

The rise in a zero coupon bond's value from its discounted purchase price towards par over the holding period is known as:

Capitalisation of unpaid coupons

Which three characteristics distinguish zero coupon bonds from all coupon-bearing bonds?

No default risk, minimum duration, and tax-exempt interest income

No reinvestment risk, maximum duration, and phantom income taxation

No credit risk, variable duration, and deferred capital gains treatment

No liquidity risk, moderate duration, and preferential dividend rates

Which pairing correctly matches a zero coupon bond's defining advantage with its defining risk?

Eliminates interest rate risk but carries the maximum reinvestment risk

Eliminates default risk but carries the maximum inflation risk

Eliminates reinvestment risk but carries the maximum interest rate risk

Eliminates liquidity risk but carries the maximum currency risk

Zero coupon instruments are created in which two primary ways?

Government auction of discount notes, or private placement of new paper with dealers

Direct issuance as a zero, or converting an issuer's preferred shares into discount debt

Exchange listing of discount paper, or securitisation of pooled mortgage loans by agencies

Direct issuance as a zero, or stripping coupons from existing Treasury bonds

Treasury STRIPS are created when primary dealers do what to a Treasury note or bond?

Combine several Treasury issues into a single pooled certificate

Separate each coupon and principal payment into its own security

Guarantee the coupon payments on behalf of a corporate issuer

Exchange short-dated bills for longer-dated notes at auction

A thirty-year Treasury bond is stripped. How many individual instruments result?

Thirty-one, one for every year plus redemption

Sixty, one for every semi-annual interest date

Sixty-one, one for every scheduled cash flow

Thirty, one for every year until redemption

The price of a zero coupon bond equals its face value divided by which quantity?

The coupon rate multiplied by the number of periods remaining

One minus the yield to maturity, raised to the number of periods

The current market rate multiplied by the years already elapsed

One plus the yield to maturity, raised to the number of periods

A twenty-year zero with a one thousand dollar face value and a five percent yield to maturity is priced at approximately:

Five hundred and twenty-two dollars

Six hundred and eighteen dollars

Two hundred and fourteen dollars

A client compares two twenty-year zeros of equal face value, one yielding five percent and the other six percent. Relative to the five percent bond, the six percent bond will:

Cost more today, because it promises a larger total return

Cost less today, because the face value is discounted harder

Cost the same, since both redeem at the same face value

Cost less today, but only if it is held to maturity

Reinvestment risk is the risk that:

The issuer will redeem the bond before its scheduled maturity date

Inflation will erode the purchasing power of the principal repaid

Coupon payments must be reinvested at rates below the original yield

The bond cannot be sold quickly without a large price concession

Why does a stated yield to maturity often overstate the return actually realised on a coupon-bearing bond?

It ignores the accretion of any discount at which the bond was bought

It assumes the bond will be called at the earliest permitted date

It excludes the effect of the issuer's credit rating on the price

It assumes every coupon is reinvested at the yield to maturity itself

An investor buys a twenty-year zero yielding five percent. Rates then rise to ten percent and stay there. Held to maturity, the realised annualised return is:

Five percent, because the return was locked in at purchase

Ten percent, because the bond reprices to the prevailing rate

Seven and a half percent, the average of the two rates

Below five percent, because the discount accretes more slowly

Pension funds buy zero coupon bonds maturing on known liability dates principally in order to:

Increase current income available for distribution to members

Match assets to obligations without any reinvestment risk

Reduce the duration of the overall fixed income portfolio

Obtain favourable regulatory capital treatment for those holdings

Among all bonds maturing in thirty years, a thirty-year zero coupon bond has:

A duration typical of the group

The lowest duration of any of them

The highest duration of any of them

A duration that varies with its coupon

Why does a coupon-bearing bond have a duration below its time to maturity, while a zero does not?

Its price is quoted net of accrued interest between payment dates

Its coupons are taxed annually, shortening the effective holding period

Its issuer may call it early, truncating the schedule of payments

Some of its cash flows arrive before maturity, lowering the average

Annual taxation of imputed interest on a zero coupon bond arises under which rules?

The wash sale rules governing securities repurchased within thirty days

The tax-exempt interest rules of IRC Section 103

The Original Issue Discount rules of IRC Section 1272

The passive activity rules limiting loss deductions against other income

Under the OID rules, the discount on a zero coupon bond accrues:

In equal cash instalments paid alongside the annual accrual

Entirely in the year in which the bond is finally redeemed

Only when the bond is sold before its stated maturity date

Ratably over the bond's life under the constant yield method

The holder of a taxable zero coupon bond receives which form each year?

Form 1099-OID, reporting the imputed interest accrued

Form 1099-DIV, reporting the distributions received

Form 1099-B, reporting the proceeds of any disposal

Form 1098, reporting the mortgage interest paid

Why is the phantom income problem irrelevant inside a traditional IRA?

Municipal issuers are exempt from the accrual rules entirely

No tax is owed until amounts are withdrawn from the account

The account custodian pays any tax due on the holder's behalf

Accrued discount is reclassified as a long-term capital gain

A client in a high tax bracket holds both a taxable brokerage account and a traditional IRA. Where should a taxable zero coupon bond sit?

Split evenly between the two, to average the tax outcome

In the brokerage account, where the accrual is fully deductible

In the IRA, where the accrual creates no current tax

In the brokerage account, if a municipal zero were substituted

Which zero coupon bonds remain suitable for a taxable account despite the OID rules?

Agency zeros, whose accrual is taxed at capital gains rates

Treasury zeros, whose accrual is exempt from federal tax

Corporate zeros, whose accrual is deferred until maturity

Municipal zeros, whose accrual is exempt under Section 103

Parents needing a specific sum in fifteen years buy zeros maturing in fifteen years chiefly because:

The exact amount required is certain to be available then

The bonds pay rising coupons as the date approaches

The purchase price is refunded if the child does not enrol

Tuition costs are contractually linked to prevailing bond yields

A retiree buys zeros maturing in successive years rather than a single larger holding. The purpose is to:

Reduce the credit risk attaching to any single issuer

Produce a known income stream across several future years

Qualify the portfolio for favourable estate tax treatment

Increase the average duration of the overall portfolio

A pension fund matches part of its liabilities with zeros. That protection extends to:

Every obligation falling due in the same year

The whole portfolio, once any matching is done

Only the portion of the liability actually matched

All liabilities held by the fund's insurer

A high-bracket investor holds a municipal zero coupon bond in a taxable account. Which exposure does the tax exemption leave untouched?

The need to fund a tax bill from cash the bond never pays

Reinvestment risk on the semi-annual coupon payments received

The annual income tax charge on accrued original issue discount

Maximum duration, and so the largest price fall when yields rise

Four investors each buy a ten-year zero coupon bond at a yield of six percent. Which investor's annualised return is certain to be six percent, whatever market interest rates do afterwards?

The investor who sells after five years, once market rates have risen sharply, because the price then received still reflects the six percent bought at

The investor who sells after five years, once market rates have fallen sharply, because the discount keeps accreting at the six percent bought at

The investor who holds the bond until it matures, because the price paid and the face value received settle the return in advance

The investor who sells after eight years, because with only two years left the price is set by the face value alone and no longer moves

Zero Coupon Bond: Pricing, Duration and Phantom Income

What Is a Zero Coupon Bond?

A zero coupon bond — also called a pure discount bond or deep discount bond — is a fixed income security that makes no periodic interest payments during its life and instead is issued at a price significantly below its face value, delivering the investor’s entire return through the difference between the discounted purchase price and the full face value received at maturity.

The term zero coupon reflects the fact that the bond carries a coupon rate of zero percent — no interest is paid at any point during the bond’s life. Instead the bond is purchased at a deep discount that represents the present value of the face value to be received at maturity, discounted at the bond’s yield to maturity.

The investor’s return is the difference between the purchase price and the face value — the accretion of the bond’s value from its discounted purchase price to par over the holding period — rather than periodic cash income supplemented by a capital component as with coupon-bearing bonds.

Zero coupon bonds are characterised by three defining investment characteristics that distinguish them from all coupon-bearing bonds — the complete elimination of reinvestment risk because there are no interim cash flows to reinvest, the highest interest rate sensitivity of any fixed income instrument of the same maturity because the entire economic value is concentrated in a single terminal payment making the duration equal to the time to maturity, and the phantom income tax problem that requires investors to pay annual income taxes on imputed interest that accrues each year without any corresponding cash receipt.

Zero coupon bonds are tested on the Series 65 examination in the context of fixed income products, the elimination of reinvestment risk, the relationship between duration and interest rate sensitivity, and the OID phantom income tax treatment.

How Zero Coupon Bonds Are Created and Priced

Zero coupon bonds are created in two primary ways — direct issuance by the borrower as a zero coupon instrument, or the stripping of coupon payments from existing coupon-bearing Treasury bonds through the STRIPS programme to create synthetic zero coupon instruments from each individual cash flow.

Directly issued zero coupon bonds include United States Treasury bills — which are zero coupon instruments with maturities of one year or less sold at a discount to face value — and longer-term zero coupon bonds issued by corporations and municipalities. Treasury bills are the most widely held zero coupon instruments in the world and serve as the empirical proxy for the risk-free rate in financial theory.

Treasury STRIPS — Separate Trading of Registered Interest and Principal of Securities — are created when financial institutions and dealers strip the coupon and principal payments of Treasury notes and bonds into individual zero coupon components, each of which trades as a separate zero coupon security with a specific maturity date corresponding to the date of that particular cash flow. A thirty-year Treasury bond has sixty semi-annual coupon payments plus one principal payment — stripped, these sixty-one cash flows become sixty-one separate zero coupon STRIPS with maturities ranging from six months to thirty years. The STRIPS programme is discussed in detail in the Treasury Bond and Treasury Note entries of this dictionary.

The pricing of a zero coupon bond follows directly from the present value formula — the price equals the face value divided by the quantity one plus the yield to maturity raised to the power of the number of periods to maturity.

Zero coupon bond price equals face value divided by the quantity one plus yield to maturity raised to the power of years to maturity.

A twenty-year zero coupon bond with a one thousand dollar face value and a yield to maturity of five percent is priced at one thousand divided by one point zero five raised to the twentieth power — equalling one thousand divided by two point six five three three — equalling approximately three hundred and seventy-seven dollars. An investor who pays three hundred and seventy-seven dollars today will receive one thousand dollars in twenty years — an annualised return of five percent over the full holding period.

The Elimination of Reinvestment Risk — The Defining Advantage

The most significant investment advantage of zero coupon bonds relative to coupon-bearing bonds of equivalent maturity is the complete elimination of reinvestment risk — the risk that coupon payments received during the bond’s life will be reinvested at interest rates lower than the original yield to maturity, causing the realised total return to fall below the stated YTM.

As established in the Yield to Maturity entry of this dictionary, the YTM of a coupon-bearing bond assumes that every coupon payment is reinvested at the same rate as the YTM itself. This assumption is almost never perfectly realised in practice because interest rates change continuously — when rates fall, reinvested coupons earn less than assumed, reducing the realised return below the YTM.

A zero coupon bond has no interim coupon payments to reinvest. The entire return is determined at the moment of purchase by the relationship between the purchase price and the face value — and this return is locked in for the full holding period regardless of what happens to interest rates during the intervening years. An investor who purchases a twenty-year zero coupon bond at a yield of five percent today will receive a five percent annualised return on their investment in twenty years regardless of whether interest rates rise to ten percent or fall to one percent during the holding period. This mathematical certainty of the realised return — assuming no default — makes zero coupon bonds uniquely valuable for liability-driven investing strategies where a specific dollar amount must be available at a specific future date.

Pension funds and insurance companies use zero coupon bonds extensively for liability matching — purchasing a portfolio of zero coupon bonds maturing on the dates of specific known future liability payment obligations, ensuring that the assets available on each payment date precisely match the liability due on that date without any reinvestment risk.

The Maximum Duration — The Defining Risk

While zero coupon bonds eliminate reinvestment risk entirely, they amplify interest rate risk to the maximum possible level for any fixed income instrument of equivalent maturity. A zero coupon bond’s duration — the primary measure of interest rate sensitivity — equals its time to maturity. A thirty-year zero coupon bond has a duration of thirty years — the highest duration of any bond maturing in thirty years.

The reason for this maximum duration is mathematical — duration measures the weighted average time to receipt of all cash flows. For a coupon-bearing bond, some cash flows are received before maturity in the form of coupon payments — these early cash flows reduce the weighted average time below the time to maturity. For a zero coupon bond, the only cash flow is received at maturity — the weighted average time to receipt of all cash flows equals the time to maturity exactly.

The practical consequence is that zero coupon bond prices are more sensitive to interest rate changes than any other fixed income instrument of the same maturity. A thirty-year zero coupon bond with a duration of thirty years will decline in price by approximately thirty percent if interest rates rise by one percentage point — a much larger decline than a thirty-year coupon-bearing bond with a duration of perhaps seventeen to nineteen years. As confirmed in the SEC’s investor.gov description, zero coupon bond prices fluctuate more than other types of bonds in the secondary market precisely because of this extended duration.

This maximum interest rate sensitivity makes zero coupon bonds powerful instruments for investors who want maximum duration exposure — to benefit maximally from expected interest rate declines — but also makes them dangerous for investors who do not want to bear such extreme price volatility. An investor who must sell a zero coupon bond before maturity in a rising rate environment can suffer very large capital losses relative to the purchase price.

The Phantom Income Tax Problem — The Critical Tax Disadvantage

The most significant tax disadvantage of zero coupon bonds — and the feature most critical for investment advisers to understand and communicate to clients — is the Original Issue Discount tax treatment that requires investors to pay income taxes each year on imputed interest income that accrues but is never actually received as cash until maturity.

Under IRC Section 1272 and the Original Issue Discount rules, the discount at which a zero coupon bond is purchased is treated as taxable interest income that accrues over the bond’s life using the constant yield method — even though no cash interest payment is actually made. Each year, a portion of the total discount — the difference between the purchase price and the face value — is treated as ordinary income received by the investor and reported on Form 1099-OID, requiring the investor to pay federal income tax on that phantom income in the year it accrues.

An investor who purchases a twenty-year zero coupon bond for three hundred and seventy-seven dollars will ultimately receive one thousand dollars at maturity — a total discount of six hundred and twenty-three dollars spread over twenty years of tax obligations. Each year the investor receives a Form 1099-OID reporting the imputed interest that accrued during the year and owes income tax on that amount at their applicable marginal rate — without receiving any cash to fund the tax payment. This cash-flow-negative tax obligation — paying taxes on income that has not been received as cash — makes zero coupon bonds generally inappropriate for taxable accounts.

Zero coupon bonds are generally most appropriate for tax-deferred accounts — traditional IRAs, 401(k) plans, and other retirement accounts — where the annual OID accrual does not create a current tax liability because all growth in the account is tax-deferred until distribution. In a tax-deferred account the phantom income issue is entirely irrelevant because no taxes are owed until withdrawal regardless of the character of income generated within the account.

Municipal zero coupon bonds are an exception — the tax-exempt status of municipal bond interest under IRC Section 103 extends to the OID accrual on municipal zero coupon bonds, making them appropriate for taxable accounts for investors in high marginal tax brackets who want the certainty of a known future dollar amount without the phantom income tax obligation.

Common Uses of Zero Coupon Bonds

The unique combination of zero coupon bonds’ investment characteristics — elimination of reinvestment risk, known terminal value, maximum duration, and phantom income — creates a specific set of investor applications for which zero coupon bonds are ideally suited.

College savings is a classic application — parents who know their child will need a specific sum in fifteen years can purchase zero coupon bonds maturing in fifteen years, ensuring the exact required amount will be available at the right time without any reinvestment risk from reinvesting interim coupon income. The FINRA investor education description notes specifically that zero coupon bonds are often purchased to meet a future expense such as college costs.

Retirement income planning uses zero coupon bonds to create certainty about future income — a retiree can purchase a ladder of zero coupon bonds maturing in successive years to provide a known annual income stream matching their spending needs without depending on interest rate conditions at the time of reinvestment.

Liability-driven investing for pension funds and insurance companies uses zero coupon bonds to match specific future liability payment dates — ensuring that the assets available on each date precisely equal the liability obligation due on that date, eliminating both reinvestment risk and interest rate risk for the matched portion of the liability.

Examination Relevance and Key Takeaways

Zero coupon bonds are tested on the Series 65 examination in the context of fixed income products, reinvestment risk elimination, duration and interest rate sensitivity, OID tax treatment, and appropriate use in taxable versus tax-deferred accounts.

The key points to retain are these.

A zero coupon bond pays no periodic interest — it is purchased at a discount to face value and redeems at full face value at maturity, with the discount representing the entire investment return. Zero coupon price equals face value divided by the quantity one plus YTM raised to the power of years to maturity. Treasury bills are zero coupon instruments with maturities of one year or less. Treasury STRIPS are synthetic zero coupon instruments created by stripping individual coupon and principal payments from Treasury notes and bonds.

The three defining characteristics are complete elimination of reinvestment risk — no interim coupons to reinvest means the YTM is guaranteed to be realised if held to maturity regardless of interest rate changes; maximum duration equal to time to maturity — a thirty-year zero coupon bond has duration of thirty years, producing approximately thirty percent price decline per one percentage point rise in yields — the highest interest rate sensitivity of any instrument of equivalent maturity; and phantom income OID tax treatment — IRC Section 1272 requires annual recognition and taxation of imputed interest income that accrues but is never received as cash, creating cash-flow-negative tax obligations that make zero coupon bonds generally inappropriate for taxable accounts.

Zero coupon bonds are generally most appropriate for tax-deferred retirement accounts where OID accrual creates no current tax liability, or for tax-exempt municipal zero coupon bonds in taxable accounts. Common uses include college savings funding, retirement income laddering, and institutional liability-driven investing for pension funds matching specific future payment obligations.